Fθ lens and scanning optical system using the same

ABSTRACT

An fθ lens having a skew correction function for use in a scanning optical system comprises a first lens having a negative power in a main scan plane, a second lens having a positive power in the main scan plane and arranged next to the first lens, a third lens having a toric plane and a positive power in the main scan plane and arranged next to the second lens, and an air lens formed between the first lens and the second lens having a positive power in the main scan plane.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an fθ lens used in a scanning opticalsystem, and more particularly to an fθ lens for forming a fine spot anda laser scanning optical system using the same.

2. Related Background Art

In a prior art laser scanning optical system, a laser beam emitted by alaser light source is collimated by a collimater lens, reflected by adeflector such as a polygon mirror, and a laser beam spot is formed onan image plane by a focusing lens system and it is scanned.

In such a laser scanning optical system, where the beam is scanned at aconstant angular speed such as a polygon mirror, a so-called fθ lenssystem having an fθ characteristic (a theoretical image height is givenby fθ where f is a focal distance of the optical system and θ is anincident angle) is used as a focusing lens in order to maintain theconstant speed in a main scan direction on the image plane.

In general, since the image plane which is scanned by the beam isplanar, an image plane distortion on the image plane is compensated inthe focusing lens.

Further, in order to prevent the vibration (ununiformity in pitch) ofthe scan lines on the image plane due to skew of a reflection plane of adeflector such as a polygon mirror from a predetermined position, ananamorphic optical system such as toric lens is sometimes used in thefocusing lens.

An fθ lens having three lenses in the focusing lens system in order toform a fine laser spot (less than 50 μm by a laser having a wavelengthλ=780 nm) has been proposed in U.S. Pat. No. 4,674,825. This fθ lens hasa construction shown in FIG. 1 in which a concave spherical lens 51, aconvex spherical lens 52 and a toric lens 53 are arranged in the orderfrom a mirror plane M of a deflector to an image plane I.

Data of the scanning lens shown in FIG. 1 is shown below.

                  TABLE 1                                                         ______________________________________                                        Data of Scanning Lens                                                         ______________________________________                                        R.sub.1 = -31.905                                                                             D.sub.1 = 4.70                                                                            N.sub.1 = 1.51072                                 R.sub.2 = -156.190                                                                            D.sub.2 = 2.095                                                                           N.sub.2 = 1                                       R.sub.3 = -107.660                                                                            D.sub.3 = 16.7                                                                            N.sub.3 = 1.76591                                 R.sub.4 = -52.701                                                                             D.sub.4 = 1.0                                                                             N.sub.4 = 1                                       R.sub.5.sup.( *.sup.1) = ∞                                                              D.sub.5 = 16.1                                                                            N.sub.5 = 1.78569                                 R.sub.6.sup.( *.sup.1) = -131.56                                              f = 170.4 mm       image angle ±37.5°                               F.sub.NO = 4       wavelength 780 nm                                          ______________________________________                                         .sup.( *.sup.1) Toric lens. In a subscan direction,                           R.sub.5 = -157.46                                                             R.sub.6 = -38.208                                                        

In the Table 1, Ri is a radius of curvature of the i-th lens plane ascounted from the mirror plane M of the deflector, Di is a plane-to-planedistance from the i-th lens plane to the (i+1)th lens plane, and Ni is arefractive index of a medium behind the i-th lens plane.

However, in the above three-lens fθ lens system, a spot shape ismaterially degraded and the shape may be distorted to a triangle in aperipheral area of a large image angle (scanning angle) image plane evenif the fθ characteristic, the image plane distortion and the skewcorrection are met. As a result, an effective spot diameter increases.Thus, in the prior art lens system, a high quality image is not attainedin the peripheral area of the image plane.

The image plane distortion of the fθ lens shown in FIG. 1 and the fθcharacteristic are shown in FIGS. 2 and 3. A spot shape on the imageplane at an image angle of 37 degrees is shown in FIG. 4.

As seen from those charts, the fθ characteristic and the image planedistortion are well compensated in the present example but the spotshapes of 1/e² (spot shapes from the peak intensity to 1/e² intensity)are triangular and good spot shape is not attained. As a result, in thisfθ lens, the quality of the image in the peripheral area of the imageplane is degraded.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an fθ lens to beused in a compact and high resolution scanning optical system.

In order to achieve the above object, in accordance with the presentinvention, a three-lens fθ lens including a toric lens is provided. Thefirst lens as viewed from a light incident side is one having a negativepower in a main scan plane, a second lens is one having a positive powerin the main scan plane, and the third lens is one having a tornic planeand a positive power in the main scan plane. Further, an air lens formedbetween the first lens and the second lens has a positive power in themain scan plane. As a result, the spot shape in the peripheral area ofthe image plane is kept in good quality and the scanning optical systemwhich is compact in overall scanning system and yet of high resolutionis attained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a main scan sectional view in a prior art system,

FIG. 2 shows an image plane distortion in the prior art system,

FIG. 3 shows an fθ characteristic in the prior art system,

FIG. 4 shows a spot shape at an image angle of 37 degrees in the priorart,

FIG. 5 shows a main scan sectional view in a first embodiment,

FIG. 6 shows a sub-scan sectional view in the first embodiment,

FIG. 7 shows a scanning optical system which uses the fθ lens of thepresent invention,

FIG. 8 shows an image plane distortion in the first embodiment,

FIG. 9 shows an fθ characteristic in the first embodiment,

FIG. 10 shows a spot shape at an image angle of 37 degrees in the firstembodiment,

FIG. 11 shows a main scan sectional view of a second embodiment,

FIG. 12 shows an image plane distortion in the second embodiment,

FIG. 13 shows an fθ characteristic in the second embodiment,

FIG. 14 shows a spot shape at an image angle of 37 degrees in the secondembodiment,

FIG. 15 shows a main scan sectional view of a third embodiment,

FIG. 16 shows an image plane distortion in the third embodiment,

FIG. 17 shows an fθ characteristic in the third embodiment, and

FIG. 18 shows a spot shape at an image angle of 37 degrees in the thirdembodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 5 and 6 show a first embodiment of the present invention. FIG. 5shows a sectional view of an fθ lens of the present invention, takenalong a main scan plane (which is formed by a light beam to be scannedand includes an optical axis), and FIG. 6 shows a sectional view of thefθ lens taken along a sub-scan plane (which is orthogonal to the mainscan plane and includes the optical axis).

The fθ lens 10 comprises a concave spherical lens L₁, a convex sphericallens L₂ and a toric lens L₃ arranged in this sequence as viewed from amirror plane position M of a deflector to an image plane I. A symbol cdenotes a cylindrical lens arranged between a light source such as alaser and the mirror plane position M. It has a power only in a sub-scandirection.

In FIGS. 5 and 6, r₁ and r₂ denote radii of curvature of a first planeand a second plane (counted from M) of the concave spherical lens L₁, r₃and r₄ denote radii of curvature of a third plane and a fourth plane ofthe convex spherical lens L₂, r₅₁ and r₆₁ denote radii of curvature, inthe main scan sectional plane, of a fifth plane and a sixth plane of thetoric lens L₃, and r₅₂ and r₆₂ denote radii of curvature, in thesub-scan sectional plane, of the fifth plane and the sixth plane.

FIG. 7 shows a construction of a scanning optical system which uses thefθ lens of the present invention. It comprises a light source unit 1including a light source or the light source and a collimeter lens, alinear image focusing system 2 having a cylindrical lens for linearlyfocusing a light beam emitted from the light source unit 1, and adeflector 3 having a deflecting reflection plane 3a arranged in avicinity of a position at which the light beam is linearly focused bythe linear image focusing system 2. Arranged between the deflector 3 anda medium 7 to be scanned are a spherical concave single lens 4, aspherical convex single lens 5 and a single lens 6 having a toric planewhich has a main axis and a sub-axis of different defraction powers intwo orthogonal directions. A focused spot is formed on the medium 7 bythe combined system of those lenses and the medium 7 is scanned by thespot as the deflector 3 is rotated.

The fθ lens 10 having the skew fall-down correction function comprisesthe spherical concave single lens 4, the spherical convex single lens 5and the single lens 6 having the toric plane, as described above.

The laser beam emitted from the light source is collimated by thecollimeter lens 10, linearly directed to the vicinity of the mirrorplane M of the deflector through the cylinder lens, deflected therebyand focused onto the image plane I. Thus, the laser beam is focused onthe mirror plane M of the deflector by the cylindrical lens in thesub-scan sectional plane, and then focused again by the fθ lens onto theimage plane I.

A specific example of the fθ lens is shown in Table 2, in which r₁ etc.are same as those mentioned above, d₀ is a distance between the mirrorplane M and the first plane, d_(i) (i=1˜5) is a distance between thei-th plane and the (i-1)th plane, d₆ is a distance between the sixthplane and the image plane I, n₀, n₂, n₄ and n₆ are refractive indices ofair, and n₁, n₃ and n₅ are refractive indices of the lenses L₁, L₂ andL₃, respectively.

                  TABLE 2                                                         ______________________________________                                                        d.sub.0 = 17.61                                                                            n.sub.0 = 1                                      r.sub.1 = -53.00                                                                              d.sub.1 = 4.05                                                                             n.sub.1 = 1.51                                   r.sub.2 = -186.30                                                                             d.sub.2 = 0.28                                                                             n.sub.2 = 1                                      r.sub.3 = -319.60                                                                             d.sub.3 = 8.00                                                                             n.sub.3 = 1.62                                   r.sub.4 = -49.19                                                                              d.sub.4 = 12.34                                                                            n.sub.4 = 1                                      r.sub.51 = 0                                                                  r.sub.52 = -36.05                                                                             d.sub.5 = 14.18                                                                            n.sub.5 = 1.62                                   r.sub.61 = -112.31                                                            r.sub.62 = -15.89                                                                             d.sub.6 = 97.31                                                                            n.sub.6 = 1                                      f = 100                                                                       ______________________________________                                    

As seen from Table 2, an air lens is formed between the lenses L₁ and L₂by the second plane (radius of curvature r₂) and the third plane (radiusof curvature r₃), where r₃ <r₂ <0 (that is, r₂ /r₃ ≦1). Accordingly, theair lens has a positive power.

The fact that the air lens has the positive power means that a combinedpower of the planes r₂ and r₃ is positive.

Power of plane r₂ ##EQU1##

Power of plane r₃ ##EQU2##

Combined power

    φ=φ.sub.A +φ.sub.B -eφ.sub.A φ.sub.B   (1)

where e=d₂

Accordingly the fact that the equation is positive means that the airlens has a positive power.

The image plane distortion and the fθ characteristic of the fθ lens 10are shown in FIGS. 8 and 9. It is seen that the image plane distortionand the fθ characteristic in the main scan plane and the subscan planeare good.

FIG. 10 shows the result of calculation of a spot shape at an imageangle of 37 degrees by using the fθ lens 10. The spot is elliptic (alittle longer on a sub-scan plane) at a contour line of 1/e², and it iskeep of good shape.

FIG. 11 shows a sectional view of a second embodiment of the presentinvention, taken along the main scan plane. An fθ lens 20 comprises aconcave spherical lens L₁, a convex spherical lens L₂ and a toric lensL₃, arranged in this order as viewed from a mirror plane M.

In the second embodiment, an air lens between the lenses L₁ and L₂ alsohas a positive power in the main scan plane.

A specific example of the fθ lens is shown in Table 3. The convention ofsymbols is same as that of Table 2.

                  TABLE 3                                                         ______________________________________                                                        d.sub.0 = 18.09                                                                            n.sub.0 = 1                                      r.sub.1 = -43.26                                                                              d.sub.1 = 3.00                                                                             n.sub.1 = 1.51                                   r.sub.2 = -72.12                                                                              d.sub.2 = 0.30                                                                             n.sub.2 = 1                                      r.sub.3 = -149.50                                                                             d.sub.3 = 8.49                                                                             n.sub.3 = 1.62                                   r.sub.4 = -47.52                                                                              d.sub.4 = 14.99                                                                            n.sub.4 = 1                                      r.sub.51 = 0                                                                  r.sub.52 = -35.46                                                                             d.sub.5 = 16.12                                                                            n.sub.5 = 1.62                                   r.sub.61 = -119.78                                                            r.sub.62 = -16.30                                                                             d.sub.6 = 94.27                                                                            n.sub.6 = 1                                      f = 100                                                                       ______________________________________                                    

The image plane distortion, the fθ characteristic and the spot shape atthe image angle of 37 degrees in the second embodiment are shown inFIGS. 12, 13 and 14. It is seen that, in the second embodiment, asimilar effect to that of the first embodiment is attained.

A third embodiment of th present invention is shown in FIG. 15. An fθlens 30 comprises a concave spherical lens L₁, a convex spherical lensL₂ and a toric lens L₃, arranged in this order as viewed from a mirrorplane M.

A specific example of the fθ lens 30 is shown in Table 4. The conventionof symbols is same as that in Table 2.

                  TABLE 4                                                         ______________________________________                                                        d.sub.0 = 15.62                                                                            n.sub.0 = 1                                      r.sub.1 = -62.45                                                                              d.sub.1 = 4.31                                                                             n.sub.1 = 1.51                                   r.sub.2 = 192.01                                                                              d.sub.2 = 0.11                                                                             n.sub.2 = 1                                      r.sub.3 = 192.01                                                                              d.sub.3 = 9.16                                                                             n.sub.3 = 1.62                                   r.sub.4 = -51.56                                                                              d.sub.4 = 15.19                                                                            n.sub.4 = 1                                      r.sub.51 = 0                                                                  r.sub.52 = -33.86                                                                             d.sub.5 = 14.08                                                                            n.sub.5 = 1.62                                   r.sub.61 = -120.89                                                            r.sub.62 = -15.51                                                                             d.sub.6 = 94.44                                                                            n.sub.6 = 1                                      f = 100                                                                       ______________________________________                                    

Again, in the third embodiment, r₂ =r₃ <0 (that is, r₂ /r₃ ≦1) is metand the air lens between the lenses L₁ and L₂ has a positive power.

The image plane distortion, the fθ characteristic and the spot shape atthe image angle of 37 degrees of the fθ lens 30 are shown in FIGS. 16,17 and 18, respectively. It is seen that, in the third embodiment, asimilar effect to that of the first embodiment is attained.

The fθ lens of the present invention which is used in the scanningoptical system and has the skew correction function (i.e., the fall-downcorrection due to fall-down or skew at a surface) has the first lens,the second lens and the third lens arranged in this order as viewed fromthe deflection plane. The first lens has a negative power in the mainscan plane, the second lens has a positive power in the main scan plane,the third lens has a toric plane and a positive power is the main scanplane, and the air lens between the first lens and the second lens has apositive power in the main scan plane.

Preferably, the first lens is a concave spherical lens, the second lensis a convex spherical lens and the third lens is a toric lens.

A more remarkable effect is attained when the following condition ismet:

    -2.2≦f/r.sub.3 ≦1.7

where r₂ and r₃ are radii of curvature of the concave spherical lens andthe convex spherical lens, respectively, and f is a focal distance ofthe overall lens system.

If f/r₃ deviates from the above range, the image plane distortion in themain scan plane is deteriorated and it is difficult to maintain the spotdiameter fine over the entire image plane.

More preferably, when the condition

    r.sub.2 /r.sub.3 ≦1

is met, more effect is attained.

If r₂ /r₃ >1, the power of the air lens is negative and the spot shapeis degraded.

If r₂ /r₃ <0, the spot shape is degraded. Therefore, 0≦r₂ /r₃ isdesirable.

In accordance with the fθ lens of the present invention, good spot shapeis maintained even at a large image angle area and the scanning opticalsystem which is compact and yet has a high resolution is attained.

I claim:
 1. An fθ lens having a fall-down correction function for use ina scanning optical system comprises:a first lens having a negative powerin a main scan plane; a second lens having a positive power in the mainscan plane and arranged next to said first lens; a third lens having atoric plane and a positive power in the main scan plane and arrangednext to said second lens; and an air lens formed between said first lensand said second lens having a positive power in the main scan plane. 2.An fθ lens according to claim 1 wherein said first lens is a sphericallens having a negative power, said second lens is a spherical lenshaving a positive power and said third lens is a toric lens.
 3. An fθlens according to claim 2 wherein a condition

    -2.2≦f/r.sub.3 ≦1.7

is met, where r₃ is a radius of curvature of a surface of said secondlens facing said first lens and f is a focal distance of the overalllens system.
 4. An fθ lens according to claim 3 wherein a condition

    r.sub.2 /r.sub.3 ≦1

is met, where r₂ is a radius of curvature of a surface of said firstlens facing said second lens and r₃ is a radius of curvature of asurface of said second lens facing said first lens.
 5. A scanningoptical system having a fall-down correction function comprising:a lightsource unit; a first optical system for linearly focusing a light beamemitted from said light source unit; a deflector having a deflectingreflection plane arranged in a vicinity of a linear image formed by saidfirst optical system; and a second optical system for focusing the lightbeam deflected by said deflector onto a predetermined plane; said secondoptical system having a first lens, a second lens and a third lensarranged in this sequence as viewed from said deflector, said first lenshaving a negative power in a main scan plane, said second lens having apositive power in the main scan plane, said third lens having a toricplane and a positive power in the main scan plane, and an air lensformed between said first lens and said second lens having a positivepower in the main scan plane.
 6. A scanning optical system according toclaim 5 wherein said first lens is a spherical lens having a negativepower, said second lens is a spherical lens having a positive power andsaid third lens is a toric lens.
 7. A scanning optical system accordingto claim 6 wherein a condition

    -2.2≦f/r.sub.3 ≦1.7

is met, where r₃ is a radius of curvature of a surface of said secondlens facing said first lens and f is a focal distance of the overalllens system.
 8. A scanning optical system according to claim 7 wherein acondition

    r.sub.2 /r.sub.3 ≦1

is met, where r₂ is a radius of curvature of a surface of said firstlens facing said second lens and r₃ is a radius of curvature of asurface of si second lens facing said first lens.
 9. A laser beamprinter comprising:a light source unit; a first optical system forlinearly focusing a light beam emitted from said light source unit; adeflector having a deflecting reflection plane arranged in a vicinity ofa linear image formed by said first optical system; a second opticalsystem for focusing the light beam deflected by said deflector; saidsecond optical system having a first lens, a second lens and third lensarranged in this sequence as viewed from said deflector, said first lenshaving a negative power in a main scan plane, said second lens having apositive power in the main scan plane, said third lens having a toricplane and a positive power in the main scan plane, and an air lensformed between said first lens and said second lens having a positivepower in the main scan plane, and a light reception medium for receivingthe light beam focused by said second optical system.
 10. A laser beamprinter according to claim 9 wherein said first lens is a spherical lenshaving a negative power, said second lens is a spherical lens having apositive power and said third lens is a toric lens.
 11. A laser beamprinter according to claim 10 wherein a condition

    -2.2≦f/r.sub.3 ≦1.7

is met, where r₃ is a radius of curvature of a surface of said secondlens facing said first lens and f is a focal distance of the overalllens system.
 12. A laser beam printer according to claim 11 wherein acondition

    r.sub.2 /r.sub.3 ≦1

is met, where r₂ is a radius of curvature of a surface of said firstlens facing said second lens and r₃ is a radius of curvature of asurface of said second lens facing said first lens.